Williams Crawford
06/02/2023 · Middle School

Negative Integer Exponents QuICK CneCK Which of the following is an equivalent expression to \( \frac{7^{3}}{25^{-4}} \) with only positive exponents, generated by applying the Property of Negative Integer Exponents? (1 point)

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To rewrite the expression \( \frac{7^{3}}{25^{-4}} \) with only positive exponents, we can use the property of negative exponents, which states that \( a^{-n} = \frac{1}{a^{n}} \). Starting with the expression: \[ \frac{7^{3}}{25^{-4}} \] We can rewrite \( 25^{-4} \) as \( \frac{1}{25^{4}} \). Therefore, the expression becomes: \[ \frac{7^{3}}{\frac{1}{25^{4}}} \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ 7^{3} \times 25^{4} \] Thus, the equivalent expression with only positive exponents is: \[ 7^{3} \cdot 25^{4} \]

Quick Answer

\( 7^{3} \cdot 25^{4} \)
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